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0
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I keep trying, but I can't get this.

The two solutions of the equation x^2 + bx + 18 = 0 are in the ratio of 3 to 1 for some values of b.  What is the largest possible value of b?

Nov 27, 2022

#1
+115
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Hm.. can you explain further for the 3:1 ratio is it for the variable b or the variable x?

Nov 27, 2022
#2
+115
-2

I get it now. Okay so first, look at the constant term 18. we need some 2 numbers to be in a 3:1 ratio and multiply to get 18 so

$$xy=18$$

$$4y=x$$

from this system of equations we get

$$y = \sqrt{4.5}$$

$$x = \sqrt{72}$$

these are the 2 solutions the this quadratic.

we can express this as

$$(x - \sqrt{4.5})(x-\sqrt{72}) = 0$$

so b is equal to $$\sqrt{4.5} + \sqrt{72}$$

hope this helped(i hope this is not wrong)

Nov 27, 2022